Spectral methods for cross correlations of geometric sequences

Families of sequences with low pairwise shifted cross correlations are desirable for applications such as code-division multiple-access (CDMA) communications. Often such sequences must have additional properties for specific applications. Several ad hoc constructions of such families exist in the literature, but there are few systematic approaches to such sequence design. We introduce a general method of constructing new families of sequences with bounded pairwise shifted cross correlations from old families of such sequences. The bounds are obtained in terms of the maximum cross correlation in the old family and the Walsh transform of certain functions.